Scale ingredients without changing the taste.
01 · DISCOVER
Before you begin
Enter your name and school email to save your learning. You’ll explore Proportional Relationships in Tables and then practice 12 questions with feedback.
Success criteria
- I can explain the main math idea in my own words.
- I can use a model, calculation, or example to solve a related problem.
- I can check my answers and explain why a solution makes sense.
Essential question: How can we apply ratios, fractions & equivalent ratios to solve real problems?
02 · LEARN & EXPLORE
Discover the need for ratios
A recipe uses 2 cups of oats for 3 servings. How much would 9 servings require? Ratios let us change quantities without changing the recipe.
Relate a drawing distance to a real distance.
Compare groups of different sizes.
03 · LEARN & EXPLORE
How equivalent ratios work
2:3 and 6:9 compare quantities in the same relationship. Multiply both terms by 3 to preserve the ratio. Ratios support recipes, maps, science mixtures, and proportional relationships.
04 · LEARN & EXPLORE
Build the language of proportional reasoning.
Use these terms as you explain your thinking.
A comparison of two quantities.
A number written as a quotient of two quantities.
Equal in value.
A multiplier used to enlarge or reduce quantities.
The top number in a fraction.
The bottom number in a fraction.
05 · LEARN & EXPLORE
Build a visual ratio table
| Servings | 3 | 6 | 9 |
|---|---|---|---|
| Cups | 2 | 4 | 6 |
Each new column multiplies both quantities by the same factor.
Explore the math visually
1input units
2input units
3input units
4input units
Compare one unit with multiple units. Identify the multiplier and explain what remains constant.
Multiply both terms by the same nonzero number.
Divide both terms by the same nonzero number.
Equivalent ratios have equal unit rates or equal cross products.
06 · LEARN & EXPLORE
Scale up
Multiply both terms by the same nonzero number.
1Notice what quantities, values, or representations are given.
2Use Scale up to describe the multiplicative relationship—not only what changed.
3Check that the reasoning works for every value and that the units make sense.
Start with this foundation.
Multiply both terms by the same nonzero number.
× n07 · LEARN & EXPLORE
Scale down
Divide both terms by the same nonzero number.
1Notice what quantities, values, or representations are given.
2Use Scale down to describe the multiplicative relationship—not only what changed.
3Check that the reasoning works for every value and that the units make sense.
Build on the first idea.
Divide both terms by the same nonzero number.
÷ n08 · LEARN & EXPLORE
Verify
Equivalent ratios have equal unit rates or equal cross products.
1Notice what quantities, values, or representations are given.
2Use Verify to describe the multiplicative relationship—not only what changed.
3Check that the reasoning works for every value and that the units make sense.
Connect everything with the final idea.
Equivalent ratios have equal unit rates or equal cross products.
=09 · LEARN & EXPLORE
Worked example: Scale a recipe
- Start with 2 cups for 3 servings.
- To make 9 servings, multiply 3 by 3.
- Multiply the cups by 3 as well: 2 × 3 = 6.
- Check the equal ratios: 2/3 = 6/9.
10 · LEARN & EXPLORE
Choose the steps; use a hint if needed.
The next three problems remove some of the support. Identify what is known, select the right strategy, calculate carefully, and check the units or representation.
11 · LEARN & EXPLORE
Now complete the work independently.
Complete six questions without following a worked model. Hints remain available when you truly need them, and feedback will explain every answer.
Interactive practice tip: Use a quick sketch, table, or graph to test each answer. After selecting an answer, read the explanation and revisit your model if necessary.
12 · LEARN & EXPLORE
Reflect on ratio reasoning
Explain when to multiply both terms and how to check if a ratio stays equivalent. Describe one real-world use.
INDEPENDENT PRACTICE · 1 OF 12
Which ratio is equivalent to 3:5?
Calculate or reason before choosing your answer.
Identify the quantities and use a ratio, table, graph, or equation to justify the result.
INDEPENDENT PRACTICE · 2 OF 12
A recipe uses 4 eggs for 12 muffins. Eggs for 36 muffins?
Calculate or reason before choosing your answer.
Identify the quantities and use a ratio, table, graph, or equation to justify the result.
INDEPENDENT PRACTICE · 3 OF 12
Which fraction is equivalent to 4/6?
Calculate or reason before choosing your answer.
Identify the quantities and use a ratio, table, graph, or equation to justify the result.
INDEPENDENT PRACTICE · 4 OF 12
Scale 5:8 by a factor of three.
Calculate or reason before choosing your answer.
Identify the quantities and use a ratio, table, graph, or equation to justify the result.
INDEPENDENT PRACTICE · 5 OF 12
A map uses 2 cm for 7 km. Distance for 6 cm?
Calculate or reason before choosing your answer.
Identify the quantities and use a ratio, table, graph, or equation to justify the result.
INDEPENDENT PRACTICE · 6 OF 12
If 2/3 = x/15, find x.
Calculate or reason before choosing your answer.
Identify the quantities and use a ratio, table, graph, or equation to justify the result.
INDEPENDENT PRACTICE · 7 OF 12
Which ratio is equivalent to 2:7?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Multiply both terms by the same number.
INDEPENDENT PRACTICE · 8 OF 12
Complete 5/8 = 20/n. What is n?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
5 was multiplied by 4.
INDEPENDENT PRACTICE · 9 OF 12
A recipe uses 2 cups of rice for 6 servings. How much rice for 15 servings?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
The scale factor from 6 to 15 is 2.5.
INDEPENDENT PRACTICE · 10 OF 12
Which operation preserves the ratio 4:9?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
A ratio stays equivalent when both terms use the same multiplier.
INDEPENDENT PRACTICE · 11 OF 12
Are 14/21 and 2/3 equivalent?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Simplify 14/21.
INDEPENDENT PRACTICE · 12 OF 12
Which ratio is equivalent to 3/4?
Work independently. Select the best answer, complete any needed calculation, and check that the result fits the situation.
Return to the vocabulary and three main ideas if needed.
RESULTS · REFLECT
Your Learning Pathway Results
Reflect on your learning: Which problem best shows what you learned? What strategy helped, and what would you still like to practice? Explain your answer to a partner or write it on paper before submitting.
Check your work and submit your first-attempt score to your teacher.